Illinois Journal of Mathematics

Approximation by polynomials and Blaschke products having all zeros on a circle

David W. Farmer and Pamela Gorkin

Full-text: Open access

Abstract

We show that a nonvanishing analytic function on a sub-disc of the unit disc can be approximated by (a scalar multiple of) a Blaschke product whose zeros lie on a prescribed circle enclosing the sub-disc. We also give a new proof of the analogous classical result for polynomials. A connection is made to universality results for the Riemann zeta function.

Article information

Source
Illinois J. Math., Volume 55, Number 3 (2011), 1105-1118.

Dates
First available in Project Euclid: 29 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1369841798

Digital Object Identifier
doi:10.1215/ijm/1369841798

Mathematical Reviews number (MathSciNet)
MR3069297

Zentralblatt MATH identifier
1296.30009

Subjects
Primary: 30C15: Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) {For algebraic theory, see 12D10; for real methods, see 26C10} 30A82
Secondary: 46J15: Banach algebras of differentiable or analytic functions, Hp-spaces [See also 30H10, 32A35, 32A37, 32A38, 42B30]

Citation

Farmer, David W.; Gorkin, Pamela. Approximation by polynomials and Blaschke products having all zeros on a circle. Illinois J. Math. 55 (2011), no. 3, 1105--1118. doi:10.1215/ijm/1369841798. https://projecteuclid.org/euclid.ijm/1369841798


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References

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